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        <h3 id="基本放大電路"><a href="#基本放大電路" class="headerlink" title="基本放大電路"></a><strong>基本放大電路</strong></h3><hr>
<h4 id="放大電路的性能指標"><a href="#放大電路的性能指標" class="headerlink" title="放大電路的性能指標"></a><strong>放大電路的性能指標</strong></h4><ol>
<li><p>輸入電阻</p>
<p>輸入電阻$R_i$是從放大電路輸入端看進去的等效電阻。</p>
<script type="math/tex; mode=display">
R_i = \frac{U_i}{I_i}</script><p>由於輸入電阻的存在，使得輸入電壓和信號源電壓存在一定的偏差。為了更加不失真，在輸入電阻上的壓降應該越小越好。</p>
</li>
<li><p>輸出電阻</p>
<p>輸出電阻$R_o$是從輸出端看進去的等效電阻。</p>
<p>若$U_o^{‘}$為空載時的有效輸出電壓，$U_o$為負載為$R_L$時的有效輸出電壓。則有：</p>
<script type="math/tex; mode=display">
U_o = \frac{R_L}{R_L + R_o}U_o^{'}</script><p>所以輸出電阻</p>
<script type="math/tex; mode=display">
R_o = (\frac{U_o^{'}}{U_o} - 1)R_L</script><p>$R_o$越小，負載電阻變化時$U_o$的變化越小，放大電路的帶負載能力越強。</p>
</li>
<li><p>通頻帶</p>
<p>通頻帶用於衡量放大電路對不同頻率信號的放大能力。由於放大電路的電容、電感及半導體器件的電容等因素，放大電路只對於某一個頻率的輸入信號有放大作用，當輸入信號過高或過低時，放大倍數會下降並產生位移。對於正常範圍內的信號的放大倍數稱為<strong>中頻放大倍數</strong>。</p>
<p>使放大倍數為0.707倍中頻放大倍數的兩個頻率分別稱為<strong>下限截止頻率$f_L$</strong>和<strong>上限截止頻率$f_H$</strong>。這個頻率之間的頻率帶便稱為<strong>中頻帶</strong>或者<strong>通頻帶$f_{bw}$</strong>。</p>
</li>
<li><p>非線性失真係數</p>
<p>當輸入信號的幅度超過一定值後，輸出電壓將產生非線性失真。</p>
<p>設基波幅值為$A_1$，諧波幅值為$A_2,A_3,…$，則非線性失真係數定義為：</p>
<script type="math/tex; mode=display">
D = \sqrt{(\frac{A_2}{A_1})^2 + (\frac{A_3}{A_1})^2 + \cdots}</script><p>定義非線性失真係數的額定值，就可以算出最大不失真輸出電壓。</p>
</li>
</ol>
<hr>
<h4 id="基本共射放大電路"><a href="#基本共射放大電路" class="headerlink" title="基本共射放大電路"></a><strong>基本共射放大電路</strong></h4><p>先弄張圖鎮樓</p>
<p><img src="https://tse2-mm.cn.bing.net/th/id/OIP.5R18JZFQewMuitHZNfT8vAAAAA?w=241&amp;h=169&amp;c=7&amp;o=5&amp;dpr=1.25&amp;pid=1.7" alt=""></p>
<ol>
<li><p>設置靜態工作點的必要性</p>
<p>先約定四個物理量。在輸出信號為零時，直流電源單獨作用時的基極電流$I_B$記為$I_{BQ}$，集電極電流記為$I_{CQ}$，b-e間電壓記為$U_{BEQ}$，管壓降$U_{CE}$記為$U_{CEQ}$。</p>
<p>則有：</p>
<script type="math/tex; mode=display">
\begin{cases}
I_{BQ} = \frac{V_{BB} - U_{BEQ}}{R_b}\\
I_{CQ} = \frac{V_{CC} - U_{CEQ}}{R_c} = \beta I_{BQ}\\
\end{cases}</script><p><strong>設置靜態工作的必要性</strong>：設置靜態工作點相當於使得原輸入電流在y軸方向平行移動，通過移動輸入電流，可以使得輸入電壓盡可能地工作在放大區，使信號盡可能不失真。</p>
</li>
<li><p>基本共射放大電路的工作原理</p>
<p>當輸入端在$I_{BQ}$的基礎上疊加一個正弦電流，由於放大作用，$I_{CQ}$也會疊加一個放大了的正弦電流，而變化的$i_C$也導致了$R_C$兩段的電壓的變化，由於管壓降與$R_C$兩段的電壓之和一定，所以管壓降要在$U_{CEQ}$的基礎上疊加一個反向變化的電壓。</p>
</li>
<li><p>直接耦合共射放大電路</p>
<p><img src="https://tse4-mm.cn.bing.net/th/id/OIP.PYmYw37F4sn_0a7LxK1DPAAAAA?w=218&amp;h=193&amp;c=7&amp;o=5&amp;dpr=1.25&amp;pid=1.7" alt=""></p>
<p>在這種放大電路中，為了避免干擾，要求輸入信號、直流電源和輸出信號都有公共的接地端。因此讓基極和集電極共用一個電源。</p>
<p>則有：</p>
<script type="math/tex; mode=display">
\begin{cases}
I_{BQ} = \frac{V_{CC} - U_{BEQ}}{R_{b2}} - \frac{U_{BEQ}}{R_{b1}}\\
I_{CQ} = \frac{V_{CC} - U_{CEQ}}{R_c} - \frac{U_{CEQ}}{R_L} = \beta I_{BQ}
\end{cases}</script></li>
<li><p>阻容耦合共射放大電路</p>
<p><img src="https://tse3-mm.cn.bing.net/th/id/OIP.D9TAuv5VQRlQhAip4tNg7gHaEi?w=270&amp;h=165&amp;c=7&amp;o=5&amp;dpr=1.25&amp;pid=1.7" alt=""></p>
<p>在這種電路中，應該使得$C_1$盡可能的大，使其在輸入信號的頻率範圍內容抗很小，這樣輸入信號才能盡可能無損地得到放大。</p>
<p>當輸入端短路時，可得靜態工作點為：</p>
<script type="math/tex; mode=display">
\begin{cases}
I_{BQ} = \frac{V_{CC} - U_{BEQ}}{R_b}\\
I_{CQ} = \frac{V_{CC} - U_{CEQ}}{R_c} = \beta I_{BQ}
\end{cases}</script><p>這種電路的輸出電壓就是放大後的交流電壓，而沒有任何直流電壓。</p>
</li>
</ol>
<hr>
<h4 id="放大電路的分析方法"><a href="#放大電路的分析方法" class="headerlink" title="放大電路的分析方法"></a><strong>放大電路的分析方法</strong></h4><font size = 4>**圖解法**</font>

<ol>
<li><p>波形非線性失真的影響</p>
<ul>
<li><p>截止失真</p>
<p>由於交流輸入信號的電壓是馱載在靜態工作點進行工作的，當輸入電流變化幅度很大，而靜態工作點的電壓不高的話，輸入電壓在進入負電壓的時候，可能會導致晶體管b-e間電壓小於開啟電壓$U_{on}$，於是在輸入端就產生了一段失真。從而導致輸出端也會失真，輸出電壓由於變化方向相反，所以會產生一段<strong>頂部失真</strong>，因為晶體管進入截止區產生的失真稱為<strong>截止失真</strong>。</p>
<p><strong>這時只有提高基極電源電壓$V_{BB}$使得電壓最低時也不會截止才能防止失真。</strong></p>
</li>
<li><p>飽和失真</p>
<p>截止失真是由於基極電壓設置過低產生的，然而，如果基極電壓設置過高的話也會產生問題。當基極電壓過高時，輸入電壓在正半週期接近峰值時可能會導致<strong>基極電壓大於集電極電壓</strong>，即晶體管進入了飽和區。這樣輸入電壓在輸入端沒有失真，但是在輸出端失真了。因為晶體管進入飽和區產生的失真稱為<strong>飽和失真</strong>。</p>
<p>要消除飽和失真。可以選擇降低輸入端的靜態工作電流$I_{BQ}$，或者減小集電極電阻$R_c$以增大集電極電壓防止晶體管飽和。又或者換一個$\beta$更小的晶體管。</p>
</li>
<li><p>最大不失真輸出電壓的確定</p>
<p>總的來說，限制輸出電壓峰值的因素有兩個：$V_{CC} - U_{CEQ}、U_{CEQ} - U_{CES}(U_{CES}表示管子正常工作時在輸入端的壓降)$，超過前者引起截止失真，超過後者引起飽和失真。</p>
<p>所以$U_{omax}$的峰值應小於兩者的較小值，除以$\sqrt2$可得有效值。</p>
<p>為了使$U_{omax}$盡可能的大，$U_{CEQ}$應該盡量的設置在$U_{CES}$和$V_{CC}$的中點位置。</p>
</li>
</ul>
</li>
<li><p>直流負載線和交流負載線</p>
<p>當放大電路帶有負載$R_L$時，容易知道，輸出電壓是由集電極電流$i_c$與負載電阻$R_L$和$R_C$並聯的電阻相乘所得到的。</p>
<p>由直流通路$u_{CE} = V_{CC} - i_CR_c$所確定的負載線稱為<strong>直流負載線</strong>。</p>
<p>加上動態輸入信號的所確定的負載線稱為<strong>交流負載線</strong>。$u_{ce} = V_{CC} - i_c(R_c//R_L)$</p>
<p>交流負載線的確定方法：易知交流負載線在輸入電壓為0時，$i_c = I_{CQ},u_{ce} = U_{CEQ}$，然後確定斜率為$-(R_c//R_L)$，於是確定了交流負載線。</p>
<p>電路在帶負載$R_L$後，輸出電壓變小，其最大的峰值是$(U_{CEQ} - U_{CES})與I_{CQ}(R_c//R_L)$中的較小值。</p>
</li>
</ol>
<font size = 4>**等效電路法**</font>

<ol>
<li><p>晶體管共射h參數等效模型</p>
<p>該模型致力於用h參數來表示輸入、輸出端口的電壓、電流的關係。</p>
<p>首先，由放大電路有</p>
<script type="math/tex; mode=display">
\begin{cases}
u_{BE} = f(i_B,i_{CE})\\
i_C = f(i_B,u_{CE})
\end{cases}</script><p>式中各量均為瞬時量，為了求出變化關係，對兩式求全微分得</p>
<script type="math/tex; mode=display">
\begin{cases}
du_{BE} = \left.\frac{\partial u_{BE}}{\partial i_B}\right|_{U_{CE}}di_B + \left.\frac{\partial u_{BE}}{\partial u_{CE}}\right|_{I_B}du_{CE}\\
di_C = \left.\frac{\partial i_C}{\partial i_B}\right|_{U_{CE}}di_B + \left.\frac{\partial i_C}{\partial u_{CE}}\right|_{I_B}du_{CE}
\end{cases}</script><p>分別用$h_{11e},h_{12e},h_{21e},h_{22e}$來表示四個偏導數。e表示是共射放大電路。</p>
<p>$h_{11e}$表示$u_{CE} = U_{CEQ}$時，b-e間的動態電阻$r_{be}$。</p>
<p>$h_{12e}$表示輸出端電壓的變化對於輸入端電壓的影響，稱為<strong>內反饋係數</strong>。</p>
<p>$h_{21e}$表示$i_C$對$i_B$的導數，當小信號作用時，$h_{21e}$就近似表示電流的放大係數$\beta$。</p>
<p>$h_{22e}$表示$i_B = I_{BQ}$時c-e間的動態電阻$r_{ce}$的倒數，由於此時晶體管工作在放大區，$i_C$基本只由$i_B$決定，所以$r_{ce}$通常很大。</p>
<p><strong>$r_{be}$的近似表達式</strong></p>
<p>b-e間電阻由基區電阻$r_{bb^{‘}}$、發射結電阻$r_{b^{‘}e^{‘}}$和發射區電阻$r_e$組成。由於基區載流子濃度很小，所以基區電阻$r_{bb^{‘}}$特別大。</p>
<p>由此得$r_{be}$的近似表達式</p>
<script type="math/tex; mode=display">
r_{be}\approx r_{bb^{'}} + (1+\beta)\frac{U_T}{I_{EQ}}</script></li>
<li><p>共射放大電路動態參數的分析</p>
<ul>
<li><p>電壓放大倍數$\dot{A_u}$</p>
<p>$\dot{A_u} = \frac{\dot{U_o}}{\dot{U_i}} = -\frac{\beta R_c}{R_b + r_{be}}$</p>
</li>
<li><p>輸入電阻$R_i = R_b + r_{be}$</p>
</li>
<li><p>輸出電阻$R_o = R_c$</p>
</li>
<li><p><strong>放大的輸入電阻與信號源內阻無關，輸出電阻與負載無關</strong>。</p>
</li>
</ul>
</li>
</ol>
<hr>
<h4 id="放大電路靜態工作點的穩定"><a href="#放大電路靜態工作點的穩定" class="headerlink" title="放大電路靜態工作點的穩定"></a><strong>放大電路靜態工作點的穩定</strong></h4><ol>
<li><p>靜態工作點穩定的必要性</p>
<p>靜態工作點不但決定了電路是否會產生失真，還影響著放大倍數。在對Q點諸多的影響因素中，溫度是最主要的影響因素。</p>
<p>當溫度升高時，穿透電流$I_{CEO}$增大，表現為集電極電流$I_{CQ}$增大，晶體管的電流放大係數$\beta$增大。</p>
<p>集電極電流帶來的後果是晶體管壓降$U_{CEQ}$降低，晶體管更易進入飽和區，所以要想抵消溫度升高帶來的後果，需要較小基極電流$I_{BQ}$。</p>
<p>常用引入直流負反饋或溫度補償的方法使$I_{BQ}$在溫度變化時產生預$I_{CQ}$相反的變化。</p>
</li>
<li><p>典型的靜態工作點穩定電路</p>
<p><img src="" alt=""></p>
<p>上圖第三個為直接耦合電路和阻容耦合電路的直流通路。</p>
<p>基本思路就是在輸入端在晶體管兩端並聯一個阻值非常小的電阻，使得輸入端近似為兩個電阻的串聯，B點的電位$U_{BQ}$始終近似等於$R_{b1}$兩端的電壓，不受環境溫度的影響。</p>
<p>當溫度升高時，發射極電流增大，由於發射極又串聯了一個$R_e$才接地，所以$R_e$和$R_c$壓降的增大導致發射極電位升高。發射極電位升高，基極電位基本不變，所以$U_{BE}$減小，所以$I_B$急劇減小，$I_C$也隨之減小，從而實現了負反饋的效果。</p>
<p>理論上，$R_e$越大，$I_C$只要有非常微小的變化就能帶來很大的負反饋，Q點越穩定。但是$R_e$太大往往會使晶體管容易進入飽和區。</p>
<p><strong>靜態工作點的估算</strong></p>
<p>首先</p>
<script type="math/tex; mode=display">
U_{BQ} \approx \frac{R_{b1}}{R_{b1} + R_{b2}}V_{CC}</script><p>發射極電流</p>
<script type="math/tex; mode=display">
I_{EQ} = \frac{U_{BQ} - U_{BEQ}}{R_e}</script><p>利用$I_{CQ}\approx I_{EQ}$，可得</p>
<script type="math/tex; mode=display">
U_{CEQ} \approx V_{CC} - I_{CQ}(R_e + R_c)</script><p><strong>動態工作點的估算</strong></p>
<p>分為加旁路電容和不加旁路電容。還是那一套，懶得寫了。</p>
</li>
<li><p>穩定靜態工作點的措施</p>
<p><img src="" alt=""></p>
<p>在使用溫度補償的方法來穩定靜態工作點時，利用$V_{CC}$和$V_{BEQ}$的比值的懸殊，可以得出</p>
<script type="math/tex; mode=display">
I_{R_b} = \frac{V_{CC} - U_{BEQ}}{R_b} \approx \frac{V_{CC}}{R_b}</script><p>$I_{R_b}$是流過輸入端靜態電路上的分壓電阻$R_b$的電流，這個電流在流過$R-b$後分作兩頭，一頭就是靜態穩定電流$I_{BQ}$，另一頭頂著二極管的陰極就進去了，稱之為二極管的反向電流$I_R$。</p>
<p>當溫度升高時，$I_{CQ}$增大，而$I_{R_b}$由於基本不受溫度影響所以可看作基本不變。反向電流$I_R$同樣因為溫度升高而增大，這就導致$I_{BQ}$降低，從而導致$I_{CQ}$降低，從而達到負反饋的效果。</p>
</li>
</ol>
<hr>
<h4 id="晶體管放大電路的三種基本接法"><a href="#晶體管放大電路的三種基本接法" class="headerlink" title="晶體管放大電路的三種基本接法"></a><strong>晶體管放大電路的三種基本接法</strong></h4><p>基本接法分別是共射、共基、共集。</p>
<ol>
<li><p>基本共集放大電路</p>
<p><img src="https://img-blog.csdn.net/20180502111145873?watermark/2/text/aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzI5NTQ1MjMx/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70" alt="這張圖找了好久"></p>
<p>基本共集放大電路第一眼看上去很難與基本共射放大電路相區分。仔細看發現共集在集電極後面接了個$R_e$的電阻，而原來的$R_c$電阻不見了，並且輸出電壓就是$R_e$兩端的電壓。</p>
<p><strong>靜態分析</strong></p>
<p>對於圖(b)的輸入迴路</p>
<script type="math/tex; mode=display">
V_{BB} = I_{BQ}R_b + U_{BEQ} + I_{EQ}R_e</script><p>所以</p>
<script type="math/tex; mode=display">
\begin{cases}
I_{BQ} = \frac{V_{BB} - U_{BEQ}}{R_b + (1+\beta)R_e}\\
U_{CEQ} = V_{CC} - (1+\beta)I_{BQ}R_e
\end{cases}</script><p><strong>動態分析</strong></p>
<p>說實話要把(a)想象成(c)圖有點困難，其實只要把$V_{CC}$短路，再把三極管箭頭的方向改一下就好了。</p>
<p>電壓放大倍數</p>
<script type="math/tex; mode=display">
\begin{aligned}\dot{A}_u &= \frac{\dot{U}_O}{\dot{U}_i}\\
&=\frac{I_eR_e}{I_{b}(R_b+r_{be})  + I_{e}R_e}\\
&=\frac{(1+\beta)R_e}{R_b + r_{be} + (1+\beta)R_e}
\end{aligned}</script><p>然後不要忘了</p>
<script type="math/tex; mode=display">
r_{be} \approx r_{bb^{'}} + \beta \frac{U_T}{I_{CQ}}</script><p>我們驚奇地發現電壓放大倍數是小於1的，只有在$(1+\beta)R_e &gt;&gt; R_b + r_{be}$時才能接近1。所以常稱共集放大電路為<strong>射極跟隨器</strong>。</p>
<p>儘管電壓沒有放大，但是電流$R_e$相比$R_b$是有放大的，所以電路具有功率放大作用。</p>
<p><strong>輸入電阻</strong></p>
<script type="math/tex; mode=display">
R_i = R_b + r_{be} + (1+\beta)R_e</script><p><strong>輸出電阻</strong></p>
<p>為了計算輸出電阻，可以將輸入端電壓短路，輸出端加一個變化的電壓$\dot{U}_o$。</p>
<p>不難計算出</p>
<script type="math/tex; mode=display">
R_o = \frac1{\frac1{R_e} + (1+\beta)\frac1{R_b + r_{be}}} = \frac{R_e(R_b + r_{be})}{(1+\beta)R_e+R_b+r_{be}} = \frac{R_e(R_b+r_{be})}{R_i}</script><p>可以看出共集放大電路是屬於輸入電阻大，輸出電阻小的電路。</p>
</li>
<li><p>基本共基放大電路</p>
<p><img src="https://tse3-mm.cn.bing.net/th?id=OIP.LOOGoiMJeqCA3M_VzKPULAHaGO&amp;pid=Api&amp;rs=1" alt=""></p>
<p>對於直流通路</p>
<script type="math/tex; mode=display">
I_{BQ} = \frac{V_{BB} - U_{BEQ}}{R_e}\\
U_{CEQ} = V_{CC} + V_{BB} - (1+\beta)I_{BQ}R_c - I_{BQ}R_e</script><p>對於交流通路</p>
<script type="math/tex; mode=display">
\dot{A}_u = \frac{\dot{U}_o}{\dot{U}_i} = \frac{\beta \dot{I_b}R_c}{\dot{I}_br_{be} + (1+\beta)\dot{I}_bR_e}  = \frac{\beta R_c}{r_{be} + (1+\beta)R_e}\\
R_i = R_e + \frac{r_{be}}{1+\beta}\\
R_o = R_c</script><p>由於共基電路的輸入電流為$i_E$，輸出電流為$i_C$。所以沒有電流放大能力。</p>
<p>當$R_e$為信號源內阻時，電路的電壓放大倍數為$\beta R_c/r_{be}$，所以有電壓放大能力。</p>
<p>此外，由於$\dot{A}_u$為正數，說明輸入電壓與輸出電壓的變化方向是相同的，即同相。共基電路的最大優點是頻帶寬，因而常用於無線通信。</p>
</li>
<li><p>三種接法的比較</p>
<ul>
<li>共射電路既能放大電流又能放大電壓，輸入電阻居三種電路之中，輸出電阻較大，頻帶交債。常作為低頻電壓放大電路的單元電路。</li>
<li>共集電路不能放大電壓只能放大電流，在三種電路中輸入電阻最大、輸出電阻最小。並具有電壓跟隨的特點。常作為電壓放大電路的輸入級和輸出級。</li>
<li>共基電路只能放大電壓不能放大電流，輸入電阻小，電壓放大倍數和輸出電阻與共射電路相當。在三種電路中高頻特性最好，常作為寬頻放大電路。</li>
</ul>
</li>
</ol>

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            <p>原文作者：<a href="http://xiaoqixian.github.io.com">XiaoQixian</a>
            <p>原文链接：<a href="http://xiaoqixian.github.io.com/2020/04/12/%E5%9F%BA%E6%9C%AC%E6%94%BE%E5%A4%A7%E9%9B%BB%E8%B7%AF/">http://xiaoqixian.github.io.com/2020/04/12/%E5%9F%BA%E6%9C%AC%E6%94%BE%E5%A4%A7%E9%9B%BB%E8%B7%AF/</a>
            <p>发表日期：<a href="http://xiaoqixian.github.io.com/2020/04/12/%E5%9F%BA%E6%9C%AC%E6%94%BE%E5%A4%A7%E9%9B%BB%E8%B7%AF/">April 12th 2020, 11:59:59 pm</a>
            <p>更新日期：<a href="http://xiaoqixian.github.io.com/2020/04/12/%E5%9F%BA%E6%9C%AC%E6%94%BE%E5%A4%A7%E9%9B%BB%E8%B7%AF/">April 13th 2020, 12:20:28 am</a>
            <p>版权声明：本文采用<a rel="license noopener" href="http://creativecommons.org/licenses/by-nc/4.0/" target="_blank">知识共享署名-非商业性使用 4.0 国际许可协议</a>进行许可</p>
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